Controlling electron transport through a single-molecule device is key to the realization of nanoscale electronic components. A design requirement for single molecule electrical devices is that the molecule must be both structurally and electrically connected to the metallic electrodes. Typically, the mechanical and electrical contacts are achieved by the same chemical moiety. In this study, we demonstrate that the structural role may be played by one group (for example, a sulfide) while the electrical role may be played by another (a conjugated chain of C═C π-bonds). We can specify the electrical conductance through the molecule by modulating to which particular site on the oligoene chain the electrode binds. The result is a device that functions as a potentiometer at the single-molecule level.